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The World of Illusion Knitting

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PICKING UP THREADS

This was written in
2007
so is now very dated

Two things happened almost simultaneously and they intertwined. One involved the Curator of the Mathematics Collection of the Science Museum in London; the other involved Sir Roger Penrose. Everyone has heard of the Science Museum but, unless you have an interest in science or maths, you may not have heard of Sir Roger Penrose. Many would argue that he is the greatest living British mathematician. He is very highly-respected in his own right though to some he is best known for his partnerships with others. He was Stephen Hawking’s partner in the writing of A Brief History of Time. The Penrose family worked very closely with M C Escher and many of his well-known drawings are based on ideas that originated with the Penroses. For example, the staircase that appears to go both up and down at the same time is known as the Penrose Staircase. Sir Roger definitely has a very artistic streak.

Much of Sir Roger’s work was involved with discovering shapes that fit together. Whereas we played with anything that took our fancy, he worked very seriously within strict self-imposed limits. He had made many well-documented discoveries. After hearing that we were working with shapes whose angles had to be a multiple of 45 degrees, he sent us a sheet of paper which was completely covered in squares and 45 degree rhombuses in a random manner. There was no repeat to the tiling as it moved across the page. He had annotated the drawing and outlined a small area in blue and, around that a larger green area, to show what he had discovered. It was complicated stuff. The part that was easiest to grasp was that this was an aperiodic tiling, which means that it does not repeat across the surface. You can look this up in books where you will find detailed ways to annotate and define the properties of shapes – a bit like those of the man who worked on his own at our first Easter Conference.

We were back in the realms of dealing with intellectual, academic mathematicians who knew far more than we did. This was a little daunting but our incomplete understanding didn’t deter us. We studied the subject long enough to understand a little more then returned to the tiling. Steve wanted to colour it but before he could do that he had to redraw it on the computer, which was quite a tedious task as there were hundreds of tiles.

There is something known as the Four-Colour Map Theorem which says that any map, or other kind of picture, can be coloured using just four colours without two pieces next to each other having the same colour. Steve knew that the design would certainly need no more than four colours. It only needed three. He coloured it in red, yellow and orange. The original tiling was even more outstanding than before.

We had a dilemma about how to use it. We couldn’t use it all. There was far too much and knitted pieces would have been tediously small to make. Also, it wouldn’t have a straight edge as the pieces poked out at the sides, so it would be difficult to hang.

Eventually we decided to take a section which made a unit in itself. In a way this was a disservice to the original but we do include a copy of the complete coloured-in version in the instruction booklet so if anyone has the urge to try it all they can.

The area we took is circular, with an uneven edge where the shapes stick out. It has 160 pieces which make up eight sections. In these eight sections there are four of one arrangement and four of another. They fit together to make a design that repeats four times around the circle.

It is circular and looks a bit like a flower. There was only one choice for its name. It had to be Penrose.

At around the same time the Curator from the Science Museum got in touch, by email. She had heard of our work and wanted to buy Square Deal for the museum. Despite our resolution never to sell it would have been rather churlish to turn down such a request. It was time to make an exception. You may remember, from near the beginning of this story, that Square Deal was stapled to a board and hung in my classroom. Because it was small it had stayed there ever since, gathering dust. I offered to make a new version for the museum but they insisted that they wanted the original, and that they would also like to buy Counting Pane and Pythagoras Tree.

Square Deal was unpicked from its board. The dust was vacuumed out of it and it was stuffed in a bag, along with the other two pieces and I set off to deliver them.

Click here to see more about Penrose

12b. ART OR SCIENCE? continued